?? maybe take very scattered, ambitious approach ... ??? ... ??with alleged excuse of preparing for summer course, in part ?? ...
?? 2 in some way related themes??? :
1 ideal with invertible underlying module .....
2 forcing ideal to have invertible underlying module ...
(??then even more general, invertibleness of modules not associated with ideals ... ??? .... and renormalization ... ?? ... ???)
??? so maybe... try to concentrate on theme 1, though try to _briefly_ mention theme 2 ...
?? ideal class groups of quadratic number fields ... relating to modular forms ... ??? ...
?? also ideal class groups of cyclotomic number fields ... ??relating to toric stuff ??? ....
?? ideal class groups of affine curves ??? .... ?? getting into geometric interpretation and theme 2 a bit ... ??? so maybe back off a bit ??? .... ???
or maybe don't ... ???? ....
???base change stuff ???? ....
?? dimensional theory of fractional ideals ... ???toric analogs?? ....
???? "galois stack" ... ????.....
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